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Symmetrised M-estimators of multivariate scatter. (English) Zbl 1122.62048

Summary: We introduce a family of symmetrised M-estimators of multivariate scatter. These are defined to be M-estimators only computed on pairwise differences of the observed multivariate data. The symmetrised Huber’s M-estimator and L. Dümbgen’s [Ann. Inst. Stat. Math. 50, No. 3, 471–491 (1998; Zbl 0912.62061)] estimator serve as our examples. The influence functions of the symmetrised M-functionals are derived and the limiting distributions of the estimators are discussed in the multivariate elliptical case to consider the robustness and efficiency properties of estimators. The symmetrised M-estimators have the important independence property; they can therefore be used to find the independent components in the independent components analysis (ICA).

MSC:

62H12 Estimation in multivariate analysis
62G35 Nonparametric robustness
62E20 Asymptotic distribution theory in statistics
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference

Citations:

Zbl 0912.62061

Software:

FastICA
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References:

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